The two main concepts of Rigidity Theory are rigidity, where the framework has no continuous deformation, and global rigidity, where the given distance set determines the locations of the points up to isometry. We consider the following augmentation problem. Given a graph G=(V, E) which is generically rigid in the plane, find a minimum cardinality edge set F such that the graph G'=(V, E \cup F) is generically globally rigid in the plane. We provide a min-max theorem and a polynomial time algorithm for this problem.

A joint work with András Mihálykó.